Julian Vill

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math.AC2023

Bounds on Hilbert functions with application to convexity

Julian Vill

Given a subspace $U \subset C [x_{1}, \dots, x_{n}]_{d}$ we consider the closure of the image of the rational map $P^{n - 1} ⇢ P^{d i m U - 1}$ given by $U$ .…

math.AC2021

Ideals of Spaces of Degenerate Matrices

Julian Vill, Mateusz Michałek, Alexander Taveira Blomenhofer

The variety $Sing_{n, m}$ consists of all tuples $X = (X_{1}, \dots, X_{m})$ of $n \times n$ matrices such that every linear combination of $X_{1}, \dots, X_{m}$ is singula…